# Neglecting all losses, the developed torque (T) of a DC separately excited motor, operating under constant terminal voltage, is related to its output power (P) as under:

Neglecting all losses, the developed torque (T) of a DC separately excited motor, operating under constant terminal voltage, is related to its output power (P) as under:

### Right Answer is: T ∝ P

#### SOLUTION

Relation of output power and torque under constant terminal voltage can be given as

The torque developed by a d.c motor is directly proportional to Flux per pole × Armature Resistance i.e

T ∝ ΦIa
T ∝ Ia———1

Output power for the separately excited motor is given as

P = EbIa.

If voltage supply is constant then power is

P ∝ Ia……………. (2)

From equation (1) and (2),

T ∝ P.

or

Consider a pulley of radius r meter acted upon by a circumferential force of F Newton which causes it to rotate at N r.p.m.

The angular speed of the pulley is

Work done by this force in one revolution

= Force × distance = F × 2πR Joule

The power developed = Work Done/Time

= (F × 2πR)/60/N

= (F × R) × (2πN)/60

The power developed = T × ω watt or P = T ω Watt

From the relation of power developed in the armature is equivalent to mechanical torque developed, is

P = T × ω

Where
P = Output power of separately excited motor and it is given as P = EbIa
ω = Angular speed in rad/sec. and it is given as ω = 2πN ⁄ 60

where N = Speed of motor in rpm,
Eb = induced back emf,
Ia = armature current.

If voltage supply is constant then power is

∴ T∝ power output P will be equal to power developed in the armature.
∴ T ∝ P.

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